Estimation of linear and log-linear trend in the data and forecastinggasoline sales in US.

The following table shows gasoline sales in the United States (in millions of barrels) from thefirst quarter of 1986 to the last quarter of 1989.Gasoline sales in the United States: 1986:1 To 1989:4(in millions of barrels)1986.1 600.4 1987.1 610.8 1988.1 640.8 1989.1 639.31986.2 652.8 1987.2 679.5 1988.2 686.5 1989.2 681.01986.3 671.1 1987.3 681.2 1988.3 691.1 1989.3 685.51986.4 654.8 1987.4 667.6 1988.4 676.5 1989.4 677.7a.Estimate the linear trend in the data, and use it to forecast gasoline sales in the United Statesin each quarter of 1990.

b.Estimate the log-linear trend in the data, and use it to forecast gasoline sales in the UnitedStates in each quarter of 1990.

c.Which form of the trend fits the historical data better? Why would we expect both forecaststo be rather poor?

Sub: Economics Topic:Econometrics

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The Homework solutions from Classof1 are intended to help the student understand the approach to solving the problem and not for submitting the same inlieu of your academic submissions for grades.

Solution:

a.Estimation of Linear trend lineT

t

= b

0

+b

1

t

T

t

= Trend value in period tb

0

= intercept of the lineb

1

= Slope of the trend linet = timeT

t

= 649.204+1.91tForecast of each quarter of 1990T

17(1990.1)

= 649.204+1.91*17 = 681.504T

18(1990.2)

= 649.204+1.91*18 = 683.584T

19(1990.3)

= 649.204+1.91*19 = 685.494T

20(1990.4)

= 649.204+1.91*20 = 687.404

Sub: Economics Topic:Econometrics

*

The Homework solutions from Classof1 are intended to help the student understand the approach to solving the problem and not for submitting the same inlieu of your academic submissions for grades.